It is well-known that a single machine scheduling problem of minimizing the total tardiness is NP-hard. Recently, Liu, Ng and Cheng solved some special hierarchical minimization problems with total tardiness as the primary criterion by the Algorithm TAP (Two Assignment Problems) in O(n3) time....

It is known that the single machine scheduling problem of minimizing the number of tardy jobs is polynomially solvable. However, it becomes NP-hard if each job has a deadline. Recently, Huo et al. solved some special cases by a backwards scheduling approach. In this note we present a dual...